Bhashya
ना च पुरुषश्चकेसरी च सिंहश्च नृकेसरी ।तत्र पुरुषमित्यनूद्य सत्यं परंब्रह्म जानीयादिति विधीयते ।एतदुक्तं भवति— सत्यस्यपरब्रह्मणः स्वमायया लीलाविग्रहं पुरुषाकारं ऋतमितिपरमार्थे जानीयादिति यावत् ।यद्वा, ऋत सत्यं परं ब्रह्मब्रह्मात्मकं पुरुषाकारं ओमित्योंकारेण व्याख्यातम् , ऋत-मिति धननाम ऋतमयं हिरण्मयं हिरण्यमयं जानीयादि-त्यर्थः ।अत एव सतो बन्धुमिति बन्धुरिति धननाम ब्रह्म-णो विवर्त हिरण्मयम् असति ब्रह्मणि हृदि निरविन्दन्नितिकैश्चिद्व्याख्यातम् ।कृष्णपिंङ्गलं कृष्णपिङ्गले अक्षिणी यस्य तंतथोक्तम् ।ऊर्ध्वरेतमिति च्छान्दसम् ।ऊर्ध्वरेतस्कं योगा-रूढमासीनं विरूपाक्षं ललाटनेत्रम् . ललाटनेत्रेण रौद्रता प्रा-प्नोति तद्व्यावृत्त्यर्थं शंकरं सुखकरं वरदाभयहस्तं शकरसाह-चर्यान्नीललोहितमिति नीलकण्ठम् उर्वरितप्रदेशे लोहितम् ।नीललोहितौ वर्णौ ललाटनेत्रयोर्यथायोग्यतयस्य धृतौ तथो-क्तम् ।कल्पान्तरे तु श्वेतवर्णम् ; एवं सुवर्णलोहितशुक्लाकाराणांविकल्पः कामनावशाद्व्यवस्थितः ।उमापतिं उमा गौरीतस्याः पतिः तम् ।'श्रियं लक्ष्मीम्' इति सप्त शक्तयो वक्ष्यन्ते ।पशुपतिः पशूनां प्राणिनां पतिः, यद्वा पशूनां वेदानां गाय-त्र्यादीनाम्, 'पशवो वै छन्दांसि' इति श्रुतेः ।पिनाकिनंपिनाकधनुर्हस्तम् ।हीति निश्चितार्थः ।अमितद्युतिम् अमित-प्रकाशम् ।ईशानः सर्वविद्यानां प्रभुः ।ईश्वरः सर्वभूतानांप्रभुः ।ब्रह्माधिपतिः, ब्रह्म तपः मनसो विषयेभ्यो विवर्त्यदर्शनं पूर्वोक्तोपासनं तस्य अधिपतिः अधिष्ठाय पाल-यिता ।ब्रह्मणोऽधिपतिः ब्रह्मणोऽधिष्ठाता ।ब्रह्मेत्यन्न-नाम अन्नं क्षीरं ततश्च क्षीरस्य अधिष्ठाता ।यद्वा ब्रह्म-णः अथर्ववेदस्य अधिष्ठाता ।एवं यो यजुर्वेदवाच्यः प्रागु-क्तेन यजुषा वेदेन वाच्यः यजुर्वेदवाच्यः ।प्रागुक्तानां गुणा-नां प्रथमानिर्दिष्टानां जानीयादित्यनेनान्वयं कर्तुं विशिष्टतयाएकत्वाभिप्रायेण द्वितीयान्ततया निर्दिशति— तमिति ।सामेत्यादि गच्छतीत्यन्तम् उक्तार्थम् ।एवं प्रागुक्तमाकारंनृकेसरिण्येव जानीयात् ।अत्र केचित्प्रागुक्तमाकारं मन्त्रव-र्णात्पृथक्त्वेन उपास्यमाचक्षते ; तदयुक्तम्, एवं तर्हि उपक्रमो-पसंहाराभ्यां नृसिंहब्रह्मविद्यैक्यमवगतं बाध्येत ।नृसिंहपद-व्याख्यानावसरे नृसिंह एव आसीत्परमेश्वर इति नृसिंहेश्व-रयोः सामानाधिकरण्यमवगतं बाध्येत ।तस्मात् त्रिनेत्राद्या-कारविशिष्टः अस्यां विद्यायां नृसिंह एवोपास्य इति सिद्धम् ।
In plain words
...man, and lion, and the maned one — together, the Man-Lion. Here the verse takes up the word 'Puruṣa' again and tells us: know him as the real, the Brahman beyond all others. What this means is this — the true, supreme Brahman takes on, through its own power of māyā, a form it plays in: the shape of a person. Call that shape 'ṛta,' and know it, in the deepest sense, as that very Brahman. Or read it another way: 'ṛtam' is the true, supreme Brahman itself, Brahman through and through, wearing the shape of a person — and the syllable Om is what explains it. 'Ṛtam' is also an old word for wealth, so the line is really saying: know him as made of truth, made of gold, made of gold. That's why the phrase 'the kinsman of what is' calls him 'bandhu' — another word for wealth — the golden shining-forth of Brahman. Some teachers read the next line, 'they found it in the heart, in the Brahman beyond form,' as pointing to that same discovery. 'Kṛṣṇapiṅgala' is simply: the one whose two eyes are black and tawny. 'Ūrdhvaretas' is an old Vedic word for one who holds his vital energy upward — deep in yoga, seated, his eyes uneven because a third eye sits on his forehead. A forehead-eye alone would make him look fearsome, so to soften that he is also called Śaṅkara, the bringer of good, the bringer of joy, his hands raised in the gestures that grant a boon and dispel fear. And because of that same word, 'Nīlalohita' means the blue-throated one — blue at the throat, red everywhere else — the two colors sitting exactly where they belong, on his forehead-eye and his other eyes. In another age he wears white instead; which color he shows depends simply on what the worshipper wants. 'Umāpati' is the husband of Umā, who is Gaurī. 'Śrī' is Lakṣmī — the seven goddesses will be named later. 'Paśupati' is lord of living creatures, or, on another reading, lord of the Vedas, since scripture itself says the Vedic meters are called paśus. 'Pinākin' is the one who carries the Pināka bow. The little word 'hi' simply means 'for certain.' 'Immeasurable radiance' is just that — a light without limit. 'Īśāna' is master of every sacred science; 'Īśvara,' master of every being. 'Brahmādhipati' is the one who presides over and protects the discipline already described — the mind drawn back from the senses into that inward seeing we've called meditation; or, reading 'brahma' as its other sense, 'food' — and food here means milk — he is the one who watches over the milk itself, or over the Atharvaveda. In the same way, he is the one spoken of by the Yajurveda. All of this — every quality named so far — is gathered onto a single word, 'him,' so that everything said can be understood as pointing to one and the same being. And the line beginning 'sāma' and running to 'attains' has already been explained. Know, then, that everything said so far describes Nṛkesarin, the Man-Lion, and no one else. Some say this form belongs beside the mantra, not inside it — as though the deity described here were separate from the very words that name him. That will not do. If it were so, the unity of this teaching about Nṛsiṃha as Brahman — a unity plain from how the passage opens and how it closes — would fall apart. And when the word 'Nṛsiṃha' itself is explained, the line 'Nṛsiṃha alone was the Supreme Lord' would lose its force too, since it depends on Nṛsiṃha and Īśvara naming one and the same thing. So it stands proven: in this teaching, the one to be worshipped — three-eyed, bearing every feature just described — is Nṛsiṃha, and no one but him.
Close to the Sanskrit
...and man, and the maned one, and the lion — [thus is he called] the Man-Lion. There, having restated the word 'Puruṣa,' it is enjoined that one should know [him as] the true, the supreme Brahman. This means: one should know, in the ultimate sense, the play-form assumed by the true supreme Brahman through its own māyā — the Puruṣa-shaped one — as 'ṛta'; that much is the purport. Or else: 'ṛtam' means the true supreme Brahman, whose nature is Brahman, in the Puruṣa-shape, explained by the syllable Om. 'Ṛtam' is a name for wealth; the meaning is that one should know it as made of ṛta, made of gold, made of gold. For this very reason, the phrase 'the kinsman of the existent' — 'bandhu' being also a name for wealth — is explained by some as the golden transformation of Brahman: 'they found it in the heart, in the unmanifest Brahman' — thus explained by some. 'Kṛṣṇapiṅgala' means he whose two eyes are black-and-tawny — so called. 'Ūrdhvaretas' is a Vedic form. It means one absorbed in yoga, seated, of uneven eyes, with an eye on the forehead. Since by the forehead-eye he would acquire fierceness, to exclude that, he is called Śaṅkara, the maker of happiness, with hands making the boon-granting and fear-dispelling gestures; by association with that, 'Nīlalohita' means Nīlakaṇṭha — blue-throated, red in the rest of the body. The two colors blue and red, fittingly held on his forehead-eye and ordinary eyes, are why he is so called. But in another cosmic age, he has a white color; thus the choice among the golden, red, and white forms is fixed by the force of the worshipper's desire. 'Umāpati' — Umā is Gaurī; her husband — him. 'Śriyaṃ Lakṣmīm' — the seven powers will be described later. 'Paśupati' — lord of creatures; or else, lord of the Vedas beginning with the Gāyatrī, since the śruti says the meters, verily, are paśus. 'Pinākin' — he whose hand holds the Pināka bow. 'Hi' has the sense of certainty. 'Amitadyuti' — of immeasurable radiance. 'Īśāna' — lord of all sciences. 'Īśvara' — lord of all beings. 'Brahmādhipati' — 'brahma' means the austerity that is the previously described meditation, attained by turning the mind away from sense-objects; 'adhipati' means the one who presides over and protects it. Or: 'the overlord of Brahman' means the ruler of Brahman. 'Brahma' is also a name for food — food being milk — hence the overseer of milk; or else, the overseer of the Atharvaveda. Likewise, 'he who is denoted by the Yajurveda' is called 'yajurvedavācya.' In order to construe, by means of the verb 'one should know,' the previously stated qualities specified at the outset — specifically, with the intent of treating them as one — the text indicates them in the accusative, namely by the word 'tam.' The passage beginning 'sāma' and ending 'gacchati' has already been explained. Thus, one should know the previously described form precisely in Nṛkesarin alone. Here, some declare that the previously described form is to be worshipped as something separate from the mantra's own wording; that is untenable — for if so, the unity of the Nṛsiṃha-Brahman teaching, understood through its opening and closing, would be contradicted. At the occasion of explaining the word 'Nṛsiṃha,' the statement 'Nṛsiṃha alone was the Supreme Lord' — that is, the coreferentiality of 'Nṛsiṃha' and 'Īśvara' as understood — would likewise be contradicted. Therefore it is established that, in this teaching, it is Nṛsiṃha alone — qualified by the form beginning with three eyes — who is to be worshipped.